Question

How do you simplify `17x^2-5x-9x+5x^2-12`?

Answer 1

`17x^2-5x-9x+5x^2-12 = 17x^2+5x^2-5x-9x-12 = 22x^2-14x-12 = 2(11x^2-7x-6)`

Explanation:

First you should group like terms. That means put all of the `x^2` terms next to each other, and all of the x terms next to each other, and so on.

Then you can add the terms together. `17x^2+5x^2=22x^2`.

Finally, you can look for common factors. These aren't always helpful and different people like to stop at different points. For example, your professor might prefer the answer `22x^2-14x-12`. You should ask your professor or check the class guidelines to see what your professor wants you to do.

If you happen to notice common factors, like a factor of 2, you can "pull" them out as I have above. Notice that if you distribute the 2 you regain the full expression again.

Sometimes you can also factor the polynomial, though that isn't always easy or pretty. In this case I didn't see any simple factorization of the polynomial. You should check with your professor to see if they want you to factor the polynomial or not, and how they want you to do it.